Fast fixed-point optimization of DSP algorithms

In this paper, a fixed-point quantization noise estimator aiming at Digital Signal Processing (DSP) algorithms is presented. The estimator enables significant reduction in the computation time required to perform complex word-length optimizations while providing a high accuracy. Affine Arithmetic (AA) is used to provide a Signal-to-Quantization Noise-Ratio (SQNR) estimation for differentiable non-linear algorithms with and without feedbacks. The estimation is based on the parameterization of the statistical properties of the noise at the output of fixed-point algorithms. This parameterization allows to relate the fixed-point formats of the signals with the output noise distribution by means of fast matrix operations. Thus, a fast estimation is achieved and the word-length optimization computation time is significantly reduced. The estimator is tested using a subset of non-linear algorithms such as vector operations, power computation IIR filter, adaptive filters, and channel equalizers. The Word-length optimization computation time is boosted by three orders of magnitude while keeping the average estimation error down to 6% for most cases.